Analysis on the smoothing method for the image-linear complementarity systems Original Research Article

A smoothing method for solving the linear complementarity systems (LCS) has been proposed by Zheng in his thesis. In Zheng’s algorithm, the LCS is reformulated as a parameterized differential-algebraic equation (DAE). However, the existence of the solution of the parameterized DAE is not proved. The aim of this paper is to establish the existence of the solution of the parameterized DAE and to demonstrate the continuous dependence of the solution on the parameter and the initial value of the parameterized DAE.